Final answer:
Trent Reznor recorded 'Pretty Hate Machine' under the name Nine Inch Nails, which would become the name of his influential project.
Step-by-step explanation:
Trent Reznor recorded his album Pretty Hate Machine (1989) under the name Nine Inch Nails. This was his first major recording under this pseudonym, which went on to become the moniker for his one-man band project before it expanded into a full-fledged band. Reznor, who is primarily responsible for the band's creative direction, writes the majority of the music and lyrics, with other members contributing during live performances and some aspects of recording and production.